Temporal modes of stationary and pulsed quasistationary electromagnetic beams

We present a novel time-domain coherent-mode representation for random, stationary electromagnetic beams. We subsequently introduce random, quasistationary pulsed electromagnetic beams and develop an analogous (pseudo) mode decomposition for them as well. The former decomposition is valid provided the time window in which the field is considered is much longer than the coherence time, while the latter requires the field to vanish outside the window. For stationary beams, the theory is demonstrated by an example illustrating the role of polarization in the representation. In both cases, the data needed for the construction of the mode decomposition are straightforward to measure. The formalisms enable us to treat random vector-light beams in the time domain in terms of deterministic fields. We expect that the modal representations will find a wide range of applications in problems involving spatiotemporal propagation of temporally partially coherent light in optical systems.